Did Chesterton ever explain why he did not formally become a Catholic until long after he had starting thinking and writing for Catholics?

In all fairness, Chesterton would be the best to answer this, and there is no evidence that he was ever asked or addressed this question.

However a reasonable understanding might lie in the close association of Anglican Church to the Catholic Church. [As one Anglican said, "Its like Catholic without the Pope."]. For instance, it is easy to change houses when the difference is obvious. It is difficult when the change is minor. People are more likely to move from a 600sf 1bed/1bath home to a 1400sf 2bed/2bath home, than they are to move to another 600sf 1bed/1bath home.

Therefore with similar sacraments, priesthood, and worship, it might have been harder based on the multitude of similarities than the differences.

But lacking sufficient evidence, this should be viewed for what it is. Conjecture on my part.

I think Dr. Ian Ker's 2011 biography of Chesterton Chapter 11 ("America and Conversion") Section 6 provides us with the most objective clues. Ian began section 6 by framing the final step to follow Chesterton's own description of 3 stages of conversion which he described in his 1926 book The Catholic Church and Conversion, quoted by Dave Armstrong in his 2017 blog article Catholic Conversion: Classic Analyses (Chesterton, Belloc, Pelikan)

I think during the final stage 3 where Chesterton likens truth as a "magnet, with the powers of attraction and repulsion", he was done with the discovery process (stage 2), having no more intellectual objections, but the primary concern was to address the "repulsion" consisting primarily of his delicacies of feelings to Frances to whom he felt a tremendous debt of gratitude for having shown him a living witness of being a genuine Anglo-Catholic Christian in contrast to developments within the Church of England at the time which he disliked.

In the months preceding his reception, Ian said there were two people who helped him the most, Maurice Baring and Fr. Ronald Knox, who had travelled the same road themselves. Chesterton wrote a series of letters to Knox. In one of them (Major clue #1) Chesterton wrote:

‘I could not explain what I mean about my wife without saying much more. I see in principle it is not on the same level as the true Church; for nothing can be on the same level as God. But it is on quite a different level from social sentiments about friends and family.’

Ian Kerr wrote:

He felt a ‘responsibility’ about Frances, ‘more serious than affection, let alone passion’.

But once Frances assured one of their closest Catholic friend Fr. O'Connor (as ‘the person’ that he and Frances thought of ‘with most affection, of all who could help in such a matter') that she didn't object (out of her love and support for Chesterton), Chesterton could finally proceed. Major clue #2 from the biography:

When O’Connor arrived in Beaconsfield [on 26 July], he told Frances that there was ‘only one thing troubling Gilbert about the great step’ he was proposing to take—the effect it would have on her. ‘Oh! I shall be infinitely relieved,’ she responded. ‘You cannot imagine how it fidgets Gilbert to have anything on his mind. The last three months have been exceptionally trying. I should be only too glad to come with him, if God in His mercy would show the way clear, but up to now He has not made it clear enough to me to justify such a step.’ Having given Chesterton the reassurance he needed, O’Connor discussed at length with him ‘such special points’ as he wanted to raise, before telling him ‘to read through the Penny Catechism to make sure there were no snags to a prosperous passage’. ...

... Chesterton’s reception into the Catholic Church took place on Sunday 30 July ... While Chesterton made his confession to Father O’Connor, Frances, who was weeping, and Dom Ignatius Rice sat in the hotel bar. After conditional baptism had been administered, the two priests left Chesterton and Frances by themselves in the makeshift chapel. Returning to collect something he had forgotten, Rice saw them coming down the aisle, Chesterton with a comforting arm round his weeping wife (not all her tears were of grief, O’Connor thought).¹²² ...

The above clues bolster what @PeterTurner wrote in his answer, which in the overall scheme seems to be the primary reason of the delay, since G.K. Chesterton has shown in his thinking, feeling, and actions to be a great man of:

• intellectual integrity: the biography showed how meticulous he was in making sure he understood and agreed with everything in the catechism
• sensibilities and intuition: he worked out his inner conversion from all angles possible (see @davidlol's answer on why finally he couldn't stay in the Church of England)
• public integrity: he took the public consequences of his conversion seriously, including all impacts to his closest friends and families (the biography included a letter to his mother which he wrote immediately afterwards so his mom was among the first to know)
• deep solicitude and sensitivity to his wife Frances: the primary topic of section 6, which is corroborated by a biography of Frances and other writings quoted by @PeterTurner.

Why did it take so long for Chesterton to become Catholic?

That is a secret between the Holy Spirit and G. K. Chesterton and neither one has revealed the answer.

The operations of grace of the Holy Spirit are known unto God alone. The Holy Spirit can offer graces to a soul, but as to when, how and why they become acceptable to a soul is completely known unto God and the individual soul, otherwise Satan would try to impede his conversion to the Catholic Church.

Did Chesterton ever explain why he did not formally become a Catholic until long after he had starting thinking and writing for Catholics?

The short answer is no. He took secret with him when he died.

However, somewhere down the line he became convinced that the Catholic Church was the true Church and entered into full communion with Rome.

Chesterton wrote a book The Catholic Church and Conversion in 1926. It was not primarily about his own conversion though he acknowledged that if he was to understand the conversion of others he must try to understand his own.

The following passage records that, coming initially more from an agnostic than an Anglican perspective, he was for a long time an Anglo-Catholic. He described this as on the borderlands of Anglicanism.

He had come to believe in Catholicism and felt it would be "so much the better" if what he called "the Catholic Church" (meaning I think the true church) and "the English Church" (meaning I think the Church of England) were one and the same. Or at least that his national Church, at least the Anglo-Catholic section, was truly a part of the Catholic Church.

Later though he came to believe it was not, and that only the Church of Rome was truly Catholic.

The Church is a house with a hundred gates; and no two men enter at exactly the same angle. Mine was at least as much Agnostic as Anglican, though I accepted for a time the borderland of Anglicanism; but only on the assumption that it could really be Anglo-Catholicism. There is a distinction of ultimate intention there which in the vague English atmosphere is often missed. It is not a difference of degree but of definite aim. There are High Churchmen as much as Low Churchmen who are concerned first and last to save the Church of England. Some of them think it can be saved by calling it Catholic, or making it Catholic, or believing that it is Catholic; but that is what they want to save. But I did not start out with the idea of saving the English Church, but of finding the Catholic Church. If the two were one, so much the better; but I had never conceived of Catholicism as a sort of showy attribute or attraction to be tacked on to my own national body, but as the inmost soul of the true body, wherever it might be. It might be said that Anglo-Catholicism was simply my own uncompleted conversion to Catholicism.

Ian Ker wrote a biography of Chesterton. He records that Chesterton gave an interview to the Toronto Daily Star in which he acknowledged that "the chief Protestant leaders in the Church of England" (meaning I think those most opposed to Anglo-Catholicism) who helped him to realise that the Church of England was not a branch of the Catholic Church. Chesterton had believed in "Catholic Christianity" for 20 years but struggled to work out whether or not Anglo-Catholicism was a true expression of Catholicity. Ultimately he felt that it was not, partly at least because it did not speak authoritatively.

Although christened by the Church of England Chesterton's upbringing was amongst liberals, universalists and Unitarians. He was not himself a strong believer in any form of Christianity until he met his wife who was a very committed Anglo-Catholic and Chesterton was drawn to her religion, she being one of the few people he knew who actually practiced her religion.

Even in his younger days Chesterton had been interested in paradox, in things being opposite to common perception. He detected many elements of paradox in the attitude of his contemporary Englishmen to (Roman) Catholicism.

Roman Catholic priests were simultaneously castigated for breaking their vows of celibacy and for taking them in the first place. The general criticism of Protestants that Catholics had too little respect for the Bible rather than tradition struck him as paradoxical. This was because his generation of Protestants were themselves discovering that they were the ones who did not believe in the Bible, as Darwinism and Higher Criticim of Biblical texts became the commonly accepted view.

Catholicism was criticised as lacking in morality, since their Church required only conformance in faith. Yet in reality Chesterton felt it was Protestants who claimed to belive in Justification by Faith alone.

The Jesuits in particular were seen as devious and dishonest for their views on equivocation. Yet every gentleman expressed himself delighted to be asked to dine with a bore, and every lady admired every baby, no matter how ugly she might think it. The Jesuits were, Chesterton felt, to be admired for codifying and placing limits on a practice, equivocation, which was universal.

Nevertheless Chesterton was a journalist and sought to make sense of the world he saw. It was through his wife that he became a practicing Christian and a firm believer in (not necessarily Roman) Catholicism a great many years before deciding this meant leaving the Church of England. His wife eventually did the same four years later.